Effects of patient heterogeneity in a first-come-first-serve kidney transplant model

In this thesis, we discuss how patient death rates may affect patient choice in a kidney transplant system. Specifically, the transplant system is modeled as an M/M/1 queue with reneging, where patient and kidney arrivals are modeled as independent Poisson processes and a patient's death is referred to as reneging the queue. The patients face a problem in the form of a Markov decision process, to which we found the analytical solution when it is undiscounted and when the kidney qualities have discrete distributions. With the obtained result, we were able to examine the sensitivity analysis on the overall system. Next, we show that when the kidney distributions converge (in the sense of Kolmogorov metric), so do their associated value functions, from which we are able to extend our results to continuous distributions as well. Finally, our results are substantiated by numerical simulations.